2. (16 marks) Consider a 2-year Binomial Model for a stock is given by: Here S0=100,u=1.1 and d=u1. A risk free bond worth $100 at time 0 earns a risk free rate per period of r=0.01. put option with strike price K=$100 expiring at time 2. Denote this put option Pa. b) (2 marks) Create a replicating portfolio (0,1) at time t=0 (cash account and stock) for the option in part a). c) (2 marks) Assume the price of a call option with strike K is Cd(0)=$10 and the Delta and Gamma of the option are d=0.02 and d=0.02 respectively. Create a neutral portfolio using Cd,Pa (the option in part a) and a short position in the stock. d) (3 marks) Compute the value, at time 0, of an American put option on the stock with strike price $100 expiring at time 2. Explain at which node (s) in the tree it is optimal to exercise the American option. e) (3 marks) Assume the stock pays a one time discrete cash dividend of D=$15 at time t=1. Find the price at time 0 of an European call option expiring at time 2 with strike K=90. f) (3 marks) Assume S0 represents the exchange rate of Japanese yen per US dollar. The interest rate on yen is 1% and the interest rate on dollar is 2%. Find the price of a two-year yen denominated put option on US dollars with strike price K=100. (Use u=1.1 and d=1/u). 2. (16 marks) Consider a 2-year Binomial Model for a stock is given by: Here S0=100,u=1.1 and d=u1. A risk free bond worth $100 at time 0 earns a risk free rate per period of r=0.01. put option with strike price K=$100 expiring at time 2. Denote this put option Pa. b) (2 marks) Create a replicating portfolio (0,1) at time t=0 (cash account and stock) for the option in part a). c) (2 marks) Assume the price of a call option with strike K is Cd(0)=$10 and the Delta and Gamma of the option are d=0.02 and d=0.02 respectively. Create a neutral portfolio using Cd,Pa (the option in part a) and a short position in the stock. d) (3 marks) Compute the value, at time 0, of an American put option on the stock with strike price $100 expiring at time 2. Explain at which node (s) in the tree it is optimal to exercise the American option. e) (3 marks) Assume the stock pays a one time discrete cash dividend of D=$15 at time t=1. Find the price at time 0 of an European call option expiring at time 2 with strike K=90. f) (3 marks) Assume S0 represents the exchange rate of Japanese yen per US dollar. The interest rate on yen is 1% and the interest rate on dollar is 2%. Find the price of a two-year yen denominated put option on US dollars with strike price K=100. (Use u=1.1 and d=1/u)
